CAT 2018 Quant Questions

Question:
A right circular cone, of height 12 ft, stands on its base which has diameter 8 ft. The tip of the cone is cut off with a plane which is parallel to the base and 9 ft from the base. With π = 22/7, the volume, in cubic ft, of the remaining part of the cone is

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Correct Answer: 198

We are given that diameter of base = 8 ft. Therefore, the radius of circular base = 8/2 = 4 ft 

In triangle OAB and OCD

$\frac{OA}{AB} = \frac{OC}{CD}$

$\Rightarrow$ AB = $\frac{3×4}{12}$ = 1 ft.

Therefore, the volume of remaining part = Volume of entire cone - Volume of smaller cone

$\Rightarrow$ $\frac{1}{3}×\pi×4^2×12-\frac{1}{3}×\pi×1^2×3$

$\Rightarrow$ $\frac{1}{3}×\pi×189$

$\Rightarrow$ $\frac{22}{7×3}×189$

$\Rightarrow$ $198$ cubic ft


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